ICM25¶

Analysis of the long-term evolution of international equity markets (average returns, volatilities, long-term correlations) and economic risks of European stock markets.

Case 1: Analyzing 25 years of stock market returns¶

Analysis of the longterm evolution of international equity markets, i.e.

  • Average returns
  • Volatilities
  • Long-term correlations between markets
  • Correlation regimes

Data set (Case1.csv) includes 16 stock market indices in local currencies covering developed markets in North America, Europe and Asia-Pacific

  • Monthly stock market data starting on December 31, 1992, and ending on February 28, 2018
  • Indexed to ”100” at the beginning of the period
In [1]:
import math
import numpy as np
import pandas as pd
import plotly.express as px
In [2]:
# Metadata
data = pd.read_csv('data/Case1.csv')
# print(data.info())
# print(data.describe())
data['Date'] = pd.to_datetime(data['Date'])
  1. Display the long-term performance of the equity markets
In [3]:
data_melted = data.melt(id_vars=['Date'], value_vars=data.columns[1:], var_name='Index', value_name='Value')
fig = px.line(data_melted, x='Date', y='Value', color='Index', title='Long-term performance of the equity markets', log_y=True)
fig.show()
  1. Calculate mean returns and volatilities over the total period
In [4]:
returns = data.copy()
for index in data.columns[1:]:
    for i in range(1, len(data[index])):
        returns.loc[i, index] = np.log(data.loc[i, index] / data.loc[i - 1, index])

# First row needs to be removed as it is 100% return
returns = returns.drop(0)

# print(returns.info())
# print(returns.head())

# Mean and SD (volatility) of the returns
results_list = []
for index in returns.columns[1:]:
    mean_return = math.exp(returns[index].mean()*12)-1
    std_return = returns[index].std()*math.sqrt(12)
    results_list.append({'Index': index, 'Mean Return p.a.': mean_return, 'Volatility': std_return})

results = pd.DataFrame(results_list)
results_melted = results.melt(id_vars='Index', value_vars=['Mean Return p.a.', 'Volatility'], var_name='Metric', value_name='Value')
fig = px.bar(results_melted, x='Index', y='Value', color='Metric', barmode='group', title='Mean returns p.a. and volatilities')
fig.show()
  1. Calculate yearly returns for the stock markets
In [5]:
returns['Year'] = returns['Date'].dt.year
grouped_returns = returns.drop(columns=['Date']).groupby('Year').sum().reset_index()

fig = px.line(grouped_returns, x='Year', y=grouped_returns.columns[1:], title='Yearly returns for the stock markets')
fig.show()
  1. Calculate the correlations between the markets over the period 1993-2017
In [6]:
correlation_matrix = returns.drop(columns=['Date', 'Year']).corr()
correlation_matrix.loc['Mean'] = correlation_matrix.mean(axis=1)

fig = px.imshow(correlation_matrix, text_auto=True, title='Correlation Matrix (full)', color_continuous_scale='RdBu_r')
fig.show()
  1. Calculate the correlations for five sub-periods and analyze the correlation regimes
  • 1993-1997
  • 1998-2002
  • 2003-2007
  • 2008-2012
  • 2013-2017
In [7]:
correlation_matrix_avg = pd.DataFrame()

time_delta = 4
for year in range(1993, 2018, time_delta):
    returns_sub = returns[returns['Year'].between(year, year+time_delta)]
    correlation_matrix = returns_sub.drop(columns=['Date', 'Year']).corr()
    correlation_matrix_avg[f'{year}-{year + time_delta}'] = correlation_matrix.mean()

    fig = px.imshow(correlation_matrix, text_auto=True, title=f'Correlation Matrix ({year}-{year + time_delta})', color_continuous_scale='RdBu_r', zmin=0, zmax=1)
    fig.show()

fig = px.imshow(correlation_matrix_avg, text_auto=True, title='Average correlation over sub-periods', color_continuous_scale='RdBu_r', zmin=0, zmax=1)
fig.show()

Case 2: Rational asset pricing and multifactor models¶

Data set (Case2Factors.csv and Case2MSCI.csv) include monthly total return index data over the 1st decade of the 21st century, from January 2000 to December 2009, denominated in EUR for 10 European stock markets and 4 global risk factors.

Case2.py analyzes the relationships between the returns of the stock markets and the changes of the global factors using the following regressions for each market:

  • Market return on the MSCI World index return (single factor model)
  • Market return on the 4 global factors (4-factor model)
In [8]:
import numpy as np
import pandas as pd
import statsmodels.api as sm

Prepare MSCI world return data (Switzerland, Germany, France, UK, Japan, USA)

In [9]:
dataMSCI = pd.read_csv('data/Case2MSCI.csv')
# print(dataMSCI.info())
# print(dataMSCI.describe())
dataMSCI['Date'] = pd.to_datetime(dataMSCI['Date'])

returnsMSCI = dataMSCI.copy()
for index in dataMSCI.columns[1:]:
    for i in range(1, len(dataMSCI[index])):
        returnsMSCI.loc[i, index] = np.log(dataMSCI.loc[i, index] / dataMSCI.loc[i - 1, index])

# First row needs to be removed as it is 100% return
returnsMSCI = returnsMSCI.drop(0)

# print(returnsMSCI.info())
# print(returnsMSCI.head())

Prepare global factors return data (MSCI World, CRB Index, EUR 10Y Rate, FX USD/EUR)

In [10]:
dataFactors = pd.read_csv('data/Case2Factors.csv')
# print(dataFactors.info())
# print(dataFactors.describe())
dataFactors['Date'] = pd.to_datetime(dataFactors['Date'])

returnsFactors = dataFactors.copy()
for index in dataFactors.columns[1:]:
    for i in range(1, len(dataFactors[index])):
        returnsFactors.loc[i, index] = np.log(dataFactors.loc[i, index] / dataFactors.loc[i - 1, index])

# First row needs to be removed as it is 100% return
returnsFactors = returnsFactors.drop(0)

# print(returnsFactors.info())
# print(returnsFactors.head())

Market return on the MSCI World index return (single factor model)

In [11]:
for country in returnsMSCI.columns[1:]:
    y = returnsMSCI[country]
    X = returnsFactors['MSCI World']
    # Add a constant to the independent variable
    X = sm.add_constant(X)

    model = sm.OLS(y, X).fit()
    print(f"\n\n{"="*32} {country} {"="*33}")
    print(model.summary())

================================ Switzerland =================================
                            OLS Regression Results                            
==============================================================================
Dep. Variable:            Switzerland   R-squared:                       0.631
Model:                            OLS   Adj. R-squared:                  0.628
Method:                 Least Squares   F-statistic:                     202.0
Date:                Sun, 11 Aug 2024   Prob (F-statistic):           2.50e-27
Time:                        22:49:09   Log-Likelihood:                 273.35
No. Observations:                 120   AIC:                            -542.7
Df Residuals:                     118   BIC:                            -537.1
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const          0.0032      0.002      1.404      0.163      -0.001       0.008
MSCI World     0.6919      0.049     14.214      0.000       0.596       0.788
==============================================================================
Omnibus:                        1.468   Durbin-Watson:                   1.809
Prob(Omnibus):                  0.480   Jarque-Bera (JB):                1.024
Skew:                          -0.018   Prob(JB):                        0.599
Kurtosis:                       3.451   Cond. No.                         21.3
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.


================================ Germany =================================
                            OLS Regression Results                            
==============================================================================
Dep. Variable:                Germany   R-squared:                       0.726
Model:                            OLS   Adj. R-squared:                  0.724
Method:                 Least Squares   F-statistic:                     312.7
Date:                Sun, 11 Aug 2024   Prob (F-statistic):           5.74e-35
Time:                        22:49:09   Log-Likelihood:                 227.65
No. Observations:                 120   AIC:                            -451.3
Df Residuals:                     118   BIC:                            -445.7
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const          0.0021      0.003      0.632      0.529      -0.005       0.009
MSCI World     1.2598      0.071     17.683      0.000       1.119       1.401
==============================================================================
Omnibus:                       14.964   Durbin-Watson:                   2.272
Prob(Omnibus):                  0.001   Jarque-Bera (JB):               30.839
Skew:                          -0.472   Prob(JB):                     2.01e-07
Kurtosis:                       5.297   Cond. No.                         21.3
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.


================================ UK =================================
                            OLS Regression Results                            
==============================================================================
Dep. Variable:                     UK   R-squared:                       0.826
Model:                            OLS   Adj. R-squared:                  0.824
Method:                 Least Squares   F-statistic:                     559.2
Date:                Sun, 11 Aug 2024   Prob (F-statistic):           1.37e-46
Time:                        22:49:09   Log-Likelihood:                 303.42
No. Observations:                 120   AIC:                            -602.8
Df Residuals:                     118   BIC:                            -597.3
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const          0.0007      0.002      0.369      0.712      -0.003       0.004
MSCI World     0.8960      0.038     23.647      0.000       0.821       0.971
==============================================================================
Omnibus:                        5.877   Durbin-Watson:                   2.333
Prob(Omnibus):                  0.053   Jarque-Bera (JB):                5.334
Skew:                          -0.458   Prob(JB):                       0.0695
Kurtosis:                       3.477   Cond. No.                         21.3
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.


================================ Sweden =================================
                            OLS Regression Results                            
==============================================================================
Dep. Variable:                 Sweden   R-squared:                       0.652
Model:                            OLS   Adj. R-squared:                  0.649
Method:                 Least Squares   F-statistic:                     220.9
Date:                Sun, 11 Aug 2024   Prob (F-statistic):           8.32e-29
Time:                        22:49:09   Log-Likelihood:                 194.41
No. Observations:                 120   AIC:                            -384.8
Df Residuals:                     118   BIC:                            -379.3
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const          0.0029      0.004      0.659      0.511      -0.006       0.012
MSCI World     1.3969      0.094     14.864      0.000       1.211       1.583
==============================================================================
Omnibus:                       12.053   Durbin-Watson:                   2.158
Prob(Omnibus):                  0.002   Jarque-Bera (JB):               34.968
Skew:                           0.058   Prob(JB):                     2.55e-08
Kurtosis:                       5.642   Cond. No.                         21.3
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.


================================ Norway =================================
                            OLS Regression Results                            
==============================================================================
Dep. Variable:                 Norway   R-squared:                       0.555
Model:                            OLS   Adj. R-squared:                  0.551
Method:                 Least Squares   F-statistic:                     146.9
Date:                Sun, 11 Aug 2024   Prob (F-statistic):           1.85e-22
Time:                        22:49:09   Log-Likelihood:                 182.68
No. Observations:                 120   AIC:                            -361.4
Df Residuals:                     118   BIC:                            -355.8
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const          0.0101      0.005      2.069      0.041       0.000       0.020
MSCI World     1.2562      0.104     12.122      0.000       1.051       1.461
==============================================================================
Omnibus:                       27.978   Durbin-Watson:                   1.688
Prob(Omnibus):                  0.000   Jarque-Bera (JB):               57.320
Skew:                          -0.955   Prob(JB):                     3.57e-13
Kurtosis:                       5.796   Cond. No.                         21.3
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.


================================ France =================================
                            OLS Regression Results                            
==============================================================================
Dep. Variable:                 France   R-squared:                       0.786
Model:                            OLS   Adj. R-squared:                  0.784
Method:                 Least Squares   F-statistic:                     434.0
Date:                Sun, 11 Aug 2024   Prob (F-statistic):           2.41e-41
Time:                        22:49:09   Log-Likelihood:                 269.52
No. Observations:                 120   AIC:                            -535.0
Df Residuals:                     118   BIC:                            -529.5
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const          0.0021      0.002      0.892      0.374      -0.003       0.007
MSCI World     1.0470      0.050     20.833      0.000       0.947       1.147
==============================================================================
Omnibus:                        2.279   Durbin-Watson:                   2.394
Prob(Omnibus):                  0.320   Jarque-Bera (JB):                2.014
Skew:                          -0.045   Prob(JB):                        0.365
Kurtosis:                       3.628   Cond. No.                         21.3
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.


================================ Italy =================================
                            OLS Regression Results                            
==============================================================================
Dep. Variable:                  Italy   R-squared:                       0.630
Model:                            OLS   Adj. R-squared:                  0.627
Method:                 Least Squares   F-statistic:                     201.2
Date:                Sun, 11 Aug 2024   Prob (F-statistic):           2.89e-27
Time:                        22:49:09   Log-Likelihood:                 235.38
No. Observations:                 120   AIC:                            -466.8
Df Residuals:                     118   BIC:                            -461.2
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const          0.0014      0.003      0.446      0.657      -0.005       0.008
MSCI World     0.9476      0.067     14.186      0.000       0.815       1.080
==============================================================================
Omnibus:                        8.166   Durbin-Watson:                   2.093
Prob(Omnibus):                  0.017   Jarque-Bera (JB):               15.022
Skew:                          -0.169   Prob(JB):                     0.000547
Kurtosis:                       4.700   Cond. No.                         21.3
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.


================================ Spain =================================
                            OLS Regression Results                            
==============================================================================
Dep. Variable:                  Spain   R-squared:                       0.646
Model:                            OLS   Adj. R-squared:                  0.643
Method:                 Least Squares   F-statistic:                     215.0
Date:                Sun, 11 Aug 2024   Prob (F-statistic):           2.38e-28
Time:                        22:49:09   Log-Likelihood:                 230.99
No. Observations:                 120   AIC:                            -458.0
Df Residuals:                     118   BIC:                            -452.4
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const          0.0066      0.003      2.034      0.044       0.000       0.013
MSCI World     1.0159      0.069     14.662      0.000       0.879       1.153
==============================================================================
Omnibus:                        0.012   Durbin-Watson:                   2.125
Prob(Omnibus):                  0.994   Jarque-Bera (JB):                0.120
Skew:                           0.012   Prob(JB):                        0.942
Kurtosis:                       2.847   Cond. No.                         21.3
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.


================================ Netherlands =================================
                            OLS Regression Results                            
==============================================================================
Dep. Variable:            Netherlands   R-squared:                       0.763
Model:                            OLS   Adj. R-squared:                  0.761
Method:                 Least Squares   F-statistic:                     380.5
Date:                Sun, 11 Aug 2024   Prob (F-statistic):           1.01e-38
Time:                        22:49:09   Log-Likelihood:                 249.86
No. Observations:                 120   AIC:                            -495.7
Df Residuals:                     118   BIC:                            -490.2
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const          0.0018      0.003      0.665      0.508      -0.004       0.007
MSCI World     1.1548      0.059     19.506      0.000       1.038       1.272
==============================================================================
Omnibus:                        3.142   Durbin-Watson:                   2.120
Prob(Omnibus):                  0.208   Jarque-Bera (JB):                2.607
Skew:                          -0.339   Prob(JB):                        0.272
Kurtosis:                       3.247   Cond. No.                         21.3
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.


================================ Austria =================================
                            OLS Regression Results                            
==============================================================================
Dep. Variable:                Austria   R-squared:                       0.372
Model:                            OLS   Adj. R-squared:                  0.367
Method:                 Least Squares   F-statistic:                     69.89
Date:                Sun, 11 Aug 2024   Prob (F-statistic):           1.43e-13
Time:                        22:49:09   Log-Likelihood:                 172.24
No. Observations:                 120   AIC:                            -340.5
Df Residuals:                     118   BIC:                            -334.9
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const          0.0061      0.005      1.153      0.251      -0.004       0.017
MSCI World     0.9451      0.113      8.360      0.000       0.721       1.169
==============================================================================
Omnibus:                       42.561   Durbin-Watson:                   1.424
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              193.645
Skew:                          -1.099   Prob(JB):                     8.92e-43
Kurtosis:                       8.822   Cond. No.                         21.3
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

Market return on the 4 global factors (4-factor model)

In [12]:
for country in returnsMSCI.columns[1:]:
    y = returnsMSCI[country]
    X = returnsFactors[['FX USD/EUR', 'EUR 10Y Rate' ,'CRB Index', 'MSCI World']]
    # Add a constant to the independent variable
    X = sm.add_constant(X)

    model = sm.OLS(y, X).fit()
    print(f"\n\n{"="*32} {country} {"="*33}")
    print(model.summary())

================================ Switzerland =================================
                            OLS Regression Results                            
==============================================================================
Dep. Variable:            Switzerland   R-squared:                       0.674
Model:                            OLS   Adj. R-squared:                  0.662
Method:                 Least Squares   F-statistic:                     59.37
Date:                Sun, 11 Aug 2024   Prob (F-statistic):           4.25e-27
Time:                        22:49:09   Log-Likelihood:                 280.69
No. Observations:                 120   AIC:                            -551.4
Df Residuals:                     115   BIC:                            -537.4
Df Model:                           4                                         
Covariance Type:            nonrobust                                         
================================================================================
                   coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------
const            0.0035      0.002      1.565      0.120      -0.001       0.008
FX USD/EUR       0.2081      0.075      2.759      0.007       0.059       0.358
EUR 10Y Rate     0.0626      0.052      1.206      0.230      -0.040       0.165
CRB Index       -0.1146      0.048     -2.383      0.019      -0.210      -0.019
MSCI World       0.7431      0.053     14.017      0.000       0.638       0.848
==============================================================================
Omnibus:                        4.731   Durbin-Watson:                   1.689
Prob(Omnibus):                  0.094   Jarque-Bera (JB):                4.503
Skew:                           0.314   Prob(JB):                        0.105
Kurtosis:                       3.711   Cond. No.                         35.2
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.


================================ Germany =================================
                            OLS Regression Results                            
==============================================================================
Dep. Variable:                Germany   R-squared:                       0.807
Model:                            OLS   Adj. R-squared:                  0.800
Method:                 Least Squares   F-statistic:                     120.4
Date:                Sun, 11 Aug 2024   Prob (F-statistic):           3.73e-40
Time:                        22:49:09   Log-Likelihood:                 248.73
No. Observations:                 120   AIC:                            -487.5
Df Residuals:                     115   BIC:                            -473.5
Df Model:                           4                                         
Covariance Type:            nonrobust                                         
================================================================================
                   coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------
const            0.0019      0.003      0.655      0.514      -0.004       0.008
FX USD/EUR       0.5952      0.098      6.046      0.000       0.400       0.790
EUR 10Y Rate     0.1419      0.068      2.094      0.038       0.008       0.276
CRB Index       -0.1684      0.063     -2.684      0.008      -0.293      -0.044
MSCI World       1.3622      0.069     19.686      0.000       1.225       1.499
==============================================================================
Omnibus:                       16.175   Durbin-Watson:                   2.404
Prob(Omnibus):                  0.000   Jarque-Bera (JB):               40.147
Skew:                          -0.438   Prob(JB):                     1.92e-09
Kurtosis:                       5.695   Cond. No.                         35.2
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.


================================ UK =================================
                            OLS Regression Results                            
==============================================================================
Dep. Variable:                     UK   R-squared:                       0.839
Model:                            OLS   Adj. R-squared:                  0.834
Method:                 Least Squares   F-statistic:                     150.0
Date:                Sun, 11 Aug 2024   Prob (F-statistic):           1.16e-44
Time:                        22:49:09   Log-Likelihood:                 308.22
No. Observations:                 120   AIC:                            -606.4
Df Residuals:                     115   BIC:                            -592.5
Df Model:                           4                                         
Covariance Type:            nonrobust                                         
================================================================================
                   coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------
const            0.0005      0.002      0.279      0.781      -0.003       0.004
FX USD/EUR       0.1063      0.060      1.772      0.079      -0.013       0.225
EUR 10Y Rate     0.0983      0.041      2.381      0.019       0.017       0.180
CRB Index        0.0334      0.038      0.875      0.384      -0.042       0.109
MSCI World       0.8620      0.042     20.452      0.000       0.779       0.946
==============================================================================
Omnibus:                        7.626   Durbin-Watson:                   2.411
Prob(Omnibus):                  0.022   Jarque-Bera (JB):                7.234
Skew:                          -0.550   Prob(JB):                       0.0269
Kurtosis:                       3.489   Cond. No.                         35.2
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.


================================ Sweden =================================
                            OLS Regression Results                            
==============================================================================
Dep. Variable:                 Sweden   R-squared:                       0.696
Model:                            OLS   Adj. R-squared:                  0.685
Method:                 Least Squares   F-statistic:                     65.68
Date:                Sun, 11 Aug 2024   Prob (F-statistic):           8.24e-29
Time:                        22:49:09   Log-Likelihood:                 202.46
No. Observations:                 120   AIC:                            -394.9
Df Residuals:                     115   BIC:                            -381.0
Df Model:                           4                                         
Covariance Type:            nonrobust                                         
================================================================================
                   coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------
const            0.0018      0.004      0.424      0.673      -0.007       0.010
FX USD/EUR       0.5744      0.145      3.968      0.000       0.288       0.861
EUR 10Y Rate     0.0408      0.100      0.409      0.683      -0.157       0.238
CRB Index       -0.0427      0.092     -0.463      0.644      -0.226       0.140
MSCI World       1.4895      0.102     14.639      0.000       1.288       1.691
==============================================================================
Omnibus:                       22.814   Durbin-Watson:                   2.313
Prob(Omnibus):                  0.000   Jarque-Bera (JB):               94.146
Skew:                           0.465   Prob(JB):                     3.60e-21
Kurtosis:                       7.238   Cond. No.                         35.2
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.


================================ Norway =================================
                            OLS Regression Results                            
==============================================================================
Dep. Variable:                 Norway   R-squared:                       0.747
Model:                            OLS   Adj. R-squared:                  0.738
Method:                 Least Squares   F-statistic:                     84.70
Date:                Sun, 11 Aug 2024   Prob (F-statistic):           2.31e-33
Time:                        22:49:09   Log-Likelihood:                 216.51
No. Observations:                 120   AIC:                            -423.0
Df Residuals:                     115   BIC:                            -409.1
Df Model:                           4                                         
Covariance Type:            nonrobust                                         
================================================================================
                   coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------
const            0.0065      0.004      1.735      0.085      -0.001       0.014
FX USD/EUR       0.9059      0.129      7.036      0.000       0.651       1.161
EUR 10Y Rate     0.3405      0.089      3.843      0.000       0.165       0.516
CRB Index        0.4185      0.082      5.098      0.000       0.256       0.581
MSCI World       1.1142      0.091     12.311      0.000       0.935       1.293
==============================================================================
Omnibus:                       15.924   Durbin-Watson:                   1.868
Prob(Omnibus):                  0.000   Jarque-Bera (JB):               33.019
Skew:                          -0.509   Prob(JB):                     6.76e-08
Kurtosis:                       5.360   Cond. No.                         35.2
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.


================================ France =================================
                            OLS Regression Results                            
==============================================================================
Dep. Variable:                 France   R-squared:                       0.852
Model:                            OLS   Adj. R-squared:                  0.847
Method:                 Least Squares   F-statistic:                     165.6
Date:                Sun, 11 Aug 2024   Prob (F-statistic):           9.55e-47
Time:                        22:49:09   Log-Likelihood:                 291.60
No. Observations:                 120   AIC:                            -573.2
Df Residuals:                     115   BIC:                            -559.3
Df Model:                           4                                         
Covariance Type:            nonrobust                                         
================================================================================
                   coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------
const            0.0014      0.002      0.676      0.500      -0.003       0.005
FX USD/EUR       0.4732      0.069      6.872      0.000       0.337       0.610
EUR 10Y Rate     0.0582      0.047      1.228      0.222      -0.036       0.152
CRB Index       -0.0556      0.044     -1.266      0.208      -0.143       0.031
MSCI World       1.1211      0.048     23.160      0.000       1.025       1.217
==============================================================================
Omnibus:                       12.951   Durbin-Watson:                   2.605
Prob(Omnibus):                  0.002   Jarque-Bera (JB):               29.042
Skew:                           0.342   Prob(JB):                     4.94e-07
Kurtosis:                       5.311   Cond. No.                         35.2
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.


================================ Italy =================================
                            OLS Regression Results                            
==============================================================================
Dep. Variable:                  Italy   R-squared:                       0.706
Model:                            OLS   Adj. R-squared:                  0.696
Method:                 Least Squares   F-statistic:                     68.97
Date:                Sun, 11 Aug 2024   Prob (F-statistic):           1.16e-29
Time:                        22:49:09   Log-Likelihood:                 249.08
No. Observations:                 120   AIC:                            -488.2
Df Residuals:                     115   BIC:                            -474.2
Df Model:                           4                                         
Covariance Type:            nonrobust                                         
================================================================================
                   coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------
const           -0.0005      0.003     -0.161      0.873      -0.006       0.005
FX USD/EUR       0.5203      0.098      5.301      0.000       0.326       0.715
EUR 10Y Rate    -0.0382      0.068     -0.566      0.573      -0.172       0.096
CRB Index        0.0835      0.063      1.335      0.185      -0.040       0.207
MSCI World       1.0161      0.069     14.727      0.000       0.879       1.153
==============================================================================
Omnibus:                       17.824   Durbin-Watson:                   2.452
Prob(Omnibus):                  0.000   Jarque-Bera (JB):               76.127
Skew:                          -0.185   Prob(JB):                     2.95e-17
Kurtosis:                       6.884   Cond. No.                         35.2
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.


================================ Spain =================================
                            OLS Regression Results                            
==============================================================================
Dep. Variable:                  Spain   R-squared:                       0.737
Model:                            OLS   Adj. R-squared:                  0.727
Method:                 Least Squares   F-statistic:                     80.38
Date:                Sun, 11 Aug 2024   Prob (F-statistic):           2.13e-32
Time:                        22:49:09   Log-Likelihood:                 248.77
No. Observations:                 120   AIC:                            -487.5
Df Residuals:                     115   BIC:                            -473.6
Df Model:                           4                                         
Covariance Type:            nonrobust                                         
================================================================================
                   coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------
const            0.0057      0.003      1.964      0.052   -4.98e-05       0.011
FX USD/EUR       0.5245      0.098      5.330      0.000       0.330       0.719
EUR 10Y Rate    -0.0898      0.068     -1.325      0.188      -0.224       0.044
CRB Index       -0.1187      0.063     -1.893      0.061      -0.243       0.006
MSCI World       1.1800      0.069     17.060      0.000       1.043       1.317
==============================================================================
Omnibus:                        2.041   Durbin-Watson:                   2.419
Prob(Omnibus):                  0.360   Jarque-Bera (JB):                1.545
Skew:                           0.162   Prob(JB):                        0.462
Kurtosis:                       3.451   Cond. No.                         35.2
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.


================================ Netherlands =================================
                            OLS Regression Results                            
==============================================================================
Dep. Variable:            Netherlands   R-squared:                       0.806
Model:                            OLS   Adj. R-squared:                  0.799
Method:                 Least Squares   F-statistic:                     119.4
Date:                Sun, 11 Aug 2024   Prob (F-statistic):           5.33e-40
Time:                        22:49:09   Log-Likelihood:                 261.80
No. Observations:                 120   AIC:                            -513.6
Df Residuals:                     115   BIC:                            -499.7
Df Model:                           4                                         
Covariance Type:            nonrobust                                         
================================================================================
                   coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------
const            0.0011      0.003      0.428      0.669      -0.004       0.006
FX USD/EUR       0.4316      0.088      4.889      0.000       0.257       0.606
EUR 10Y Rate     0.0570      0.061      0.939      0.350      -0.063       0.177
CRB Index       -0.0364      0.056     -0.647      0.519      -0.148       0.075
MSCI World       1.2156      0.062     19.588      0.000       1.093       1.339
==============================================================================
Omnibus:                        1.008   Durbin-Watson:                   2.216
Prob(Omnibus):                  0.604   Jarque-Bera (JB):                0.703
Skew:                          -0.179   Prob(JB):                        0.704
Kurtosis:                       3.110   Cond. No.                         35.2
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.


================================ Austria =================================
                            OLS Regression Results                            
==============================================================================
Dep. Variable:                Austria   R-squared:                       0.607
Model:                            OLS   Adj. R-squared:                  0.593
Method:                 Least Squares   F-statistic:                     44.37
Date:                Sun, 11 Aug 2024   Prob (F-statistic):           1.75e-22
Time:                        22:49:09   Log-Likelihood:                 200.34
No. Observations:                 120   AIC:                            -390.7
Df Residuals:                     115   BIC:                            -376.7
Df Model:                           4                                         
Covariance Type:            nonrobust                                         
================================================================================
                   coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------
const            0.0020      0.004      0.468      0.641      -0.007       0.011
FX USD/EUR       1.1376      0.147      7.721      0.000       0.846       1.429
EUR 10Y Rate     0.1561      0.101      1.540      0.126      -0.045       0.357
CRB Index        0.3184      0.094      3.391      0.001       0.132       0.504
MSCI World       0.9502      0.104      9.176      0.000       0.745       1.155
==============================================================================
Omnibus:                        6.503   Durbin-Watson:                   1.871
Prob(Omnibus):                  0.039   Jarque-Bera (JB):               11.138
Skew:                          -0.004   Prob(JB):                      0.00382
Kurtosis:                       4.492   Cond. No.                         35.2
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.